Question

a) There are classes of 234 students, find the mean and standart deviation for the number born on the 4th of July.The value of the mean is mu =?

Probability
ANSWERED
asked 2021-08-08
a) There are classes of 234 students, find the mean and standart deviation for the number born on the 4th of July. Ignore leap years.The value of the mean is \(\displaystyle\mu\) = (Round to six decimal places as needed)
Yhe value of the standart deviation is \(\displaystyle\sigma\) = (Round to six decimal places as needed)
b) In a class of 234 students, would two be an unusually high number who were born on the 4th of July? Would 2 be an unussually high number of individuals who were born on the 4th of July?
A. This result is unlikely because 2 is within the range of usual values.
B. No, because 2 is within the range of usual values.
C. Yes, because 2 is greater than the maximum usual value.
D. Yes, because 2 is below the minimum usual value.

Answers (1)

2021-08-09

a) Probability of being born on 4th of July is \(\displaystyle{\frac{{{1}}}{{{365}}}}\)
Here n = 234
Mean \(\displaystyle{n}{p}={234}\cdot{\frac{{{1}}}{{{365}}}}={0.642}\)
Standart deviation \(\displaystyle=\sqrt{{{n}{p}{a}}}=\sqrt{{{234}\cdot{\frac{{{1}}}{{{365}}}}\cdot{\frac{{{364}}}{{{365}}}}}}=\sqrt{{{234}\cdot{0.003}\cdot{0.998}}}=\sqrt{{{0.7006}}}={0.838}\)
b) P (2students born on the 4th of July) \(\displaystyle={234}\cdot{\left({\frac{{{1}}}{{{365}}}}\right)}^{{2}}={7.907}\cdot{234}={0.0017}{<}{0.05}\)
It would be unusual to have two individuals born on the 4th of july
С is correct because 2 is greater than the maximum usual value

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